 Electroweak symmetry breaking

Electroweak symmetry breaking is the Higgs-field breaking $SU(2{)}_L\times U(1{)}_Y\to U(1{)}_Q$. It gives masses to the $W$ and $Z$ bosons while leaving the photon massless.

With the hypercharge convention $Q=T_3+Y$, the lower component of the Higgs doublet has $T_3=-1/2$ and $Y=1/2$. Thus $Q⟨\varphi ⟩=0$: the vacuum expectation value is electrically neutral. This is why one combination of the neutral gauge fields remains the massless photon, as the electroweak doublet gauge-boson mass matrix shows.

Continue the chosen Higgs field potential example with $g=3/5$ and $g^{\prime }=4/5$. The tree-level electroweak gauge-boson masses are $m_W=72\mathrm{GeV}$, $m_Z=120\mathrm{GeV}$ and $m_A=0$. In the $(W^3,B)$ basis,Its orthonormal eigenvectors $(4/5,3/5{)}^T$ and $(3/5,-4/5{)}^T$ have eigenvalues zero and $14400{\mathrm{GeV}}^2$. Thus $\cos {\theta }_W=3/5=m_W/m_Z$. This is an exact model check, not a fit to measured electroweak interaction parameters.

A diagonal charged-fermion Yukawa coupling expands asThe Yukawa coupling remains a free parameter: the mechanism relates a fermion mass to its scalar interaction but does not predict the numerical mass. This example concerns charged fermions; the minimal Standard Model has no right-handed neutrino and does not account for neutrino oscillations without an extension.